It might not be your brown thumb: What is Allelopathy?

If you're having trouble growing a garden it could be because your tree is poisoning it.

Norway maple (Acer platanoides) is a very common urban shade tree and it's also one naturalists love to hate.They were at the centre of last year's debacle appearing on the new $20 bill.

They do indeed come from Norway as well as other regions in Eastern Europe and Western Asia. According to Wikipedia,  it can tolerate poor, compacted soils and urban pollution. The roots of Norway maples grow very close to the ground surface, starving other plants of moisture. They also cast one of the most total and complete palls of shade over streets, lawns and gardens alike. 

Some scientists think that Norway maples might be alleopathic, meaning they poison the ground beneath them to reduce competition from other plants. The tree has been banned in New Hampshire and Massachusetts.

When plants grow in nature, they very rarely grow in patches of only one kind, the way we try to make them grow in normal agriculture. Instead we see plants growing beside other plants. A patch of woodland might have taller trees, shrubs and low plants. They interact in ways we do not yet fully understand, sometimes helping and sometimes harming one another. A group of plants that work synergistically to help each other grow is called a guild.  We can build whole forests out of guilds, such that each plant produces food, or helps those plants that do. You might be having to deal with aggressive plants like Norway Maple in your city garden right now. If you can't get rid of them, you can at least find the plants that can play well with these noxious species.

Guilding with Goutweed
Goutweed doesn't kill the plants around them, but will vigorously out-compete them for light, space and soil nutrients. Nearly impossible to weed out, goutweed will sprout back up from stem and root fragments and requires several going-overs to make sure it's really gone. From my own observation, goutweed occupies the root horizon most thickly between 1" and 5" below the surface. I have had good results with these plants that can co-exist with goutweed by occupying a different root horizon entirely, particularly deeply taprooted plants like burdock, comfrey and yellow dock. Shallow-rooted plants like geranium and english ivy manage with goutweed by occupying the root horizon of between 1" and the surface.

Guilding with Black walnut
As tasty as walnuts are, many kinds will kill the plants growing beneath and around them and can even produce an allergic reaction from their pollen in people and horses. (Wikipedia). Many plants such as tomato, potato, blackberry, blueberry, other rhododendron and heath-family plants and apple may be injured or killed within one to two months of growth within the root zone of these trees ohiostateuniversity In spite of this, walnuts are a worthwhile addition to a food forest for their tasty nuts. Fortunately there's a lot of information online about guilding with Black Walnut.

Megan of Wisconsin (she gives no last name) at the Hardy Eco Garden explains gardening with black walnut way better than I ever could so I will just reblog her entry here:

The Helpful Gardener gives a guild with black walnut that includes choke cherry, currant, goumi or sea buckthorn, elder, mulberry and wolfberry.

If you are unfortunate enough to live with  dog roses (Rosa multiflora) I hear goats will control them.

Here are some lists of species for you to try out in your food forest or garden compiled from several websites and forums

Norway maples
From adamsgardennativeplants;
Alumroot Heuchera villosa Some are native, pollinator support
American Bellflower Campanulastrum americanum Native, some pollinator support
American Pennyroyal Hedeoma pulegioides Edible and medicinal
Barren Strawberry Waldsteinia fragariodes A groundcover
Black-eyed Susan Rudbeckia hirta Pollinator support
Black Huckleberry Gaylussacia baccata native, edible berries
Christmas Fern Polystichum acrostichoides native, erosion control
European ginger Asarum europaeum Not edible, a nicely scented and well behaved groundcover that keeps down weeds
Fumewort Corydalis solida Spring ephemeral
Hairy solomon’s seal Polygonatum pubescens The solomon's seals are eaten as a tonic for general health.  The sprouts can be eaten in the springtime like fiddleheads if they are boiled in several changes of water. A spring ephemeral. Common solomon seal has done well under Norways in my garden.
Hazelnut Corylus avellana edible nut, coppice lumber  
(a note that my hazels under Norway Maples are doing poorly. It may be worth a try in a sunnier location)
Heartleaf Aster Symphyotrichum cordifolium Pollinator and calcid wasp support
sweet woodruff Galium odoratum A vigorously spreading groundcover that smells nice when dried
Largeflower bellwort Uvularia grandiflora
Lowbush Blueberry Vaccinium angustifolia native, edible fruits
Male Fern Dryopteris filix-mas Native, groundcover
Rosey sedge Carex rosea

Siberian squill Scilla sibrica Not edible, but an early spring pollinator support and spring ephemeral
Rosinweed Silphium integrifolium Pollinator support, edible seeds? oil crop?
Smooth Aster Symphyotrichum laeve Polinator and calcid wasp support
Possumhaw Viburnum Viburnum nudum Native to New England. Pollinator support. Does this indicate other viburnums such as highbush cranberry and wild raisin may also do well?
Tartan dogwood Cornus alba Dynamic accumulator
Twinleaf Jeffersonia diphylla Medicinal, native
Wild Bleeding Heart Dicentra eximia pollinator support, native
Witchhazel Hamamelis virginiana Native and medicinal
Woodland Aster Senecio sylvaticus Pollinator and calcid wasp support. It may be worth trying any sort of aster or goldenrod

From Toronto Gardens 
Chrysanthemum Pelargonium spp.
Lavender Lavandula angustifolia
Wild garlic (the species name was not given, could refer to a number of 'wild garlics')

From my own observations;

Black currant, red currant Ribes spp.
Blackberry Rubus fruticosus
Chives Allium schoenoprasum
Chrysanthemum Pelargonium spp.
Jerusalem artechoke Helianthus tuberosus
Mountain Ash Sorbus aucuparia
Nettle Urtica dioica
Mother-of-thyme Thymus praecox
Quince Cydonia oblonga
Saxifragia Stolonifera A medicinal groundcover
Solomon seal Polygonatum mutiflorum

Goutweed
Personal observations

Annual phlox ‪Phlox drummondii‬
Beach rose (Rosa rugosa) edible fruits and flowers, pollinator support, native
Blackberry, wild raspberry  Rubus fruticosus
Dog rose Rosa multiflora Edible fruit, bird habitat
High bush cranberry Viburnum trilobum
Flat topped white aster Aster umbellatus
New england aster Symphyotrichum novae-angliae
Pelargonium and geranium (just so shallow-rooted that they cannot be crowded out )
Showy goldenrod Solidago speciosa

Trees

Black spruce Picea mariana
Black ash Fraxiunus nigra
Barberry Berberis vulgaris
Elder Sambucus nigra
Lilac Syringa vulgaris
Native hawthorn Crataegus spp.
Norway Maple Acer platanoides
Poplar Populus nigra
Red oak Quercus rubens
Red maple Acer rubrum
Rowan Sorbus aucuparia
White birch Betula papyrifera
Wild Plum Prunus americana
Yellow birch Betula alleghaniensis